1. Technical Field
This disclosure relates to the design and modeling of water distribution and collection systems and, more specifically, to techniques for modeling and simulating systems that include variable speed pumps (VSPs).
2. Background
In the design and rehabilitation of water distribution and collection systems of cities, townships, and municipalities and the like, it is important to accurately predict flow and other hydraulic conditions at various points throughout the system. To make such predictions, civil engineers often turn to hydraulic modeling solutions that simulate and predict hydraulic conditions for a real-world water system, based upon a hydraulic model of the system. A hydraulic model typically includes a plurality of links (e.g., pipes) that interconnect nodes (e.g. junctions, pumps, tanks, valves, etc.)
A hydraulic solver, for example, the EPANET Solver available from the U.S Environmental Protection Agency, Washington D.C., may be employed to simulate a hydraulic model to predict flows, hydraulic pressures, and other conditions. A hydraulic solver typically solves a series of mathematical matrices descriptive of the model for various qualities given certain supplied conditions. When solving matrices for system heads and flows, many hydraulic solvers employ the well known Cholesky factorization technique.
Simulation of a hydraulic model may present various challenges depending on the components present in the model. One class of component that has presented challenges is pumps. Pumps may be classified as either constant speed, which operate at a single speed, or variable speed, which operate at different speeds using a variable speed drive (e.g., a variable frequency drive).
Generally, constant speed pumps (CSPs) are less flexible than variable speed pumps (VSPs) when serving target hydraulic characteristics in a system. CSPs operate on one characteristic curve. When a greater system resistance occurs, a CSP delivers a smaller flow. A larger flow may only be supplied with a smaller pumping head (corresponding to overcoming a smaller system resistance). This might prevent a CSP from achieving a target characteristic, for instance, moving adequate flow with target hydraulic head or moving a target flow into a system.
By contrast, a VSP may vary pump speed according to target requirements of a pumping system and thus achieve target hydraulic characteristics. For example, if the target characteristic is a nodal pressure or discharge of a water distribution or collection system, a pressure transducer may be used to regulate a variable frequency drive of the VSP. In this manner, the VSP may operate at any of a plurality of different characterises tics curves. Therefore, VSPs offer more flexibility in realizing target hydraulic characteristics than CSPs.
VSPs have previously been modeled and simulated in several ways. Commonly, an ad-hoc approach was employed, where a CSP element was manually adjusted to function akin to a VSP. For example, an engineer would manually adjust the pump speed of certain CSPs at each of a number of time steps of a simulation to ensure that a target hydraulic head was maintained at a certain location. As is apparent, such manual adjustment had a number of disadvantages. In particular, such adjustment typically required significant attention on the part of the engineer and thus was prohibitively time consuming when a large number of VSPs needed to be modeled and simulated over an extended period of time.
Another approach permitted direct calculation of a speed of a single VSP at a pump station. Details of this approach are provided in Todini et al., U.S. Pat. No. 7,013,248 titled Automatic Parameter Estimating Extension for Variable Speed Pumps, which is incorporated by reference herein. While this approach represented a significant improvement over prior techniques, it did not address all VSP configurations and operation scenarios, including multiple VSPs at one pump station, discharge side storage head control, suction side target head control, fixed-flow control and other more challenging scenarios that may occur in water distribution and collection systems.
Accordingly, what is needed is a technique for modeling and simulating water distribution and collection systems that include VSPs that is more robust and flexible than the existing techniques, to permit modeling and simulation of the more challenging scenarios that prior techniques have not been able to adequately address.